The Spectra of Local Minima in Spin-Glass Models

TL;DR

This paper investigates the spectral properties of local minima in spin-glass models, providing empirical data and asymptotic relations for key spectral characteristics as the system size grows.

Contribution

It offers the first comprehensive empirical analysis of local minima spectra in spin-glass models and derives asymptotic relations for spectral features.

Findings

Average depth of local minima characterized

Spectrum width and global minimum depth quantified

Asymptotic relations established for large N

Abstract

The spectra of spin models have been investigated in computation experiments. For the Sherrington-Kirkpatrick and Edwards-Anderson models we have determined the basic spectral characteristics: the average depth of a local minimum, the spectrum width, the depth of the global minimum. The experimental data are used to build the relations between these quantities and the model dimensionality N and find their asymptotic values for N goes to infinity.